Question: Simplify the following expression: $ q = \dfrac{r - 4}{7r - 1} + \dfrac{-5}{4} $
Answer: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{4}{4}$ $ \dfrac{r - 4}{7r - 1} \times \dfrac{4}{4} = \dfrac{4r - 16}{28r - 4} $ Multiply the second expression by $\dfrac{7r - 1}{7r - 1}$ $ \dfrac{-5}{4} \times \dfrac{7r - 1}{7r - 1} = \dfrac{-35r + 5}{28r - 4} $ Therefore $ q = \dfrac{4r - 16}{28r - 4} + \dfrac{-35r + 5}{28r - 4} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{4r - 16 - 35r + 5}{28r - 4} $ $q = \dfrac{-31r - 11}{28r - 4}$